The most eye-catching contest is a repeat of the 1999 final, with Pep Guardiola's all-conquering Bayern, who could win the Bundesliga this weekend, facing a Manchester United side who are seventh in the Premier League and struggling for form under David Moyes.
"Our staff are very thorough and will have done their homework and will be prepared for Bayern," said Manchester United club secretary John Alexander.
"If we can keep them quiet in the first leg and get an advantage then we're more than capable of stealing an away goal."
Bayern disposed of Arsenal in the previous round while United overturned a 2-0 deficit to beat Olympiacos 3-2 on aggregate.
Chelsea's match with French table-toppers PSG sees Jose Mourinho come up against one of his former players at Inter, and arguably the best centre-forward in football, in Zlatan Ibrahimovic.
The first legs of the ties are set to be played on April 1-2 with the return legs on April 8-9, with this year's final to be held at Benfica's Estadio da Luz in Lisbon on May 24.
Bayern Munich are favourites to retain their crown at 2-1, with Spanish giants Real Madrid and Barcelona priced at 4-1.
Draw in full
Barcelona v Atletico Madrid
Real Madrid v Borussia Dortmund
Paris Saint-Germain v Chelsea
Manchester United v Bayern Munich
- Sports & Recreation
- Real Madrid
- Atletico Madrid
- Manchester United
- Bayern Munich
- Pep Guardiola
- David Moyes